New ERCIM Working Group on Applications of Numerical Mathematics in Science

by Mario Arioli

At the last meeting of the ERCIM Executive Committee, the members approved the creation of a new Working Group on the Applications of Numerical Mathematics in Science.

Such a Working Group was conceived when a number of researchers, working for institutions participating directly in ERCIM, expressed their interest in building up stronger links between mathematicians within ERCIM. In particular, it was felt to be vital that a forum be created within the ERCIM institutional organisations, in which a cross-fertilisation between numerical techniques used in different fields of scientific computing might take place. The Working Group therefore intends to focus on this underpinning theme of computational and numerical mathematics. The intention is that any resulting numerical algorithm will achieve wider applicability, greater robustness, and better accuracy.

Structure of the Working Group
A preliminary survey of active researchers within ERCIM laboratories indicates that the following four major fields have strategic interest:

• Numerical Linear Algebra. Topics range from sparse matrix theory, direct and iterative solvers for large and sparse linear systems of equations, to the computation of eigenvalues and eigenvectors for large-scale problems, including the use of symbolic manipulation techniques for the solution of polynomial systems of equations.
• Numerical Solution of Differential Equations. The topics of major interest are finite-element methods, mesh generation, multigrid methods, wavelets, spectral methods and time-stepping methods.
• Continuous Optimisation and Optimal Control. Of interest here are interior point methods for large-scale linear, quadratic and nonlinear programming, SQP methods for nonlinear programming and numerical methods for optimal control.
• Large Scale Scientific Computing. In this interdisciplinary field, topics of interest include many of those cited in the previous sections, but also include parallel computing and the production of mathematical software.

There is a strong interaction between the fields; each of them frequently uses techniques developed in at least one of the others.

A number of application areas are likely to benefit from the results and activities of the Working Group, including the simulation of electromagnetic phenomena, electrical circuit theory, errors-in-variable modelling and mathematical statistics, computational chemistry, computational biology, computational materials, CFD and structural engineering, mathematics for financial derivatives, finite-element modelling for medical simulation, and environmental modelling and image processing.

The Working Group will be organised by a steering committee involving one expert from each field of interest, which will have the target of stimulating initiatives that cross the various fields. One of these representatives will be able to participate in the ERCIM organisational meeting in order to promote the initiatives of the Working Group and to discuss the budget and the resources needed to accomplish them. The table summarises the interest of each organisation, as far as we can ascertain, in each of the specific topics.

Objectives
The Working Group looks forward to broadening the scope of its main research topics into additional numerical areas. The Group strongly believes that the best way to build stronger links between the ERCIM laboratories is to encourage young scientists to act as intermediaries. The recruitment of young scientists justifies the involvement of several universities in our initiative.

Finally, the Working Group will, through its members, promote all possible initiatives within the European Programmes for Research. We will encourage grant applications and involvement in the research, technological development and demonstration (RTD) framework programmes of the European Union.

Please contact:
Mario Arioli, CLRC
Tel: +44 1235 445332
E-mail: m.arioli@rl.ac.uk